Aspects of compatibility of quantum devices and quantum communication using quantum switch [HBNI Th223]

Abstract

Incompatibility of quantum devices is one of the central features of quantum mechanics that makes it distinct from classical physics. Quantum devices are said to be incompatible if those can not be implemented simultaneously on a quantum system. These quantum devices can be measurements, channels, instruments, etc. Incompatibility of quantum devices is not only important from the foundational perspective, but also important for applications of it in di↵erent information-theoretic tasks. In the present thesis, we study several aspects of incompatibility of quantum devices.More specifically, we (1) discuss the conceptual problems in an existing definition of compatibility of quantum instruments (that we call as traditional compatibility) and show that another definition of compatibility of quantum instruments (that we call as parallel compatibility) does not have such drawbacks, (2) try to quantify and characterize the compatibility of quantum instruments, (3) study the properties of layers of classicality in the compatibility of measurements, (4) study the information loss due to quantum measurements and this study is based on the notion of measurement-channel compatibility.

Quantum switch, in the simplest scenario, is a circuit that implements indefinite causal order between two quantum channels with the help of a qubit ancilla (that we call as the control qubit) prepared in a superposed state. Quantum switch has several applications in di↵erent information-theoretic, thermodynamic tasks. In this thesis, we study the improvement in quantum communication using quantum switch. For example, we show that some useless (for communication) channels may provide useful communication under the action of quantum switch for several information-theoretic tasks: quantum random access codes, quantum steering, etc. We demonstrate that the quantum switch can also be useful in preventing the loss of coherence in a system when only coherence-breaking channels are the available channels for communication. We also show that if a useless quantum channel does not provide useful communication even after using a quantum switch, concatenating the channel with another suitable quantum channel, and subsequently using the switch, one may achieve useful communication. We are hopeful that our results will be useful for future quantum communication technology.